Local linear regression for functional data

DOI10.1007/s10463-010-0275-8zbMath1225.62093arXiv0710.5218OpenAlexW2031549309MaRDI QIDQ645536

Juan-Miguel Gracia

Publication date: 8 November 2011

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.5218

zbMATH Keywords

inverse problemmean square errorkernelsmall ball probability

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) General nonlinear regression (62J02) Applications of functional analysis in probability theory and statistics (46N30)

Related Items

Adaptive estimation in the functional nonparametric regression model ⋮ Optimal classification and nonparametric regression for functional data ⋮ Local linear regression modelization when all variables are curves ⋮ Local linear estimation of the regression function with Hilbertian variables ⋮ Spatial local linear estimation of the L₁-conditional quantiles for functional regressors ⋮ On the local linear estimate for functional regression: Uniform in bandwidth consistency ⋮ Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density ⋮ Nonparametric modelling for functional data: selected survey and tracks for future ⋮ Asymptotics of estimators for nonparametric multivariate regression models with long memory ⋮ FDA: theoretical and practical efficiency of the local linear estimation based on the kNN smoothing of the conditional distribution when there are missing data ⋮ Local polynomial modelling of the conditional quantile for functional data ⋮ Unnamed Item ⋮ Bootstrap Prediction Bands for Functional Time Series ⋮ Local linear estimation of the conditional cumulative distribution function: censored functional data case ⋮ A weighted estimator of conditional hazard rate with left-truncated and dependent data ⋮ Local linear estimate of the nonparametric robust regression in functional data ⋮ Bootstrap methods for stationary functional time series ⋮ Multivariate and functional covariates and conditional copulas ⋮ Lower bound in regression for functional data by representation of small ball probabilities ⋮ Local polynomial estimation of regression operators from functional data with correlated errors ⋮ \(k\)NN local linear estimation of the conditional cumulative distribution function: dependent functional data case ⋮ Distance-based local linear regression for functional predictors ⋮ Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density ⋮ Asymptotic normality of locally modelled regression estimator for functional data ⋮ Functional local linear estimate for functional relative-error regression ⋮ Functional data analysis: local linear estimation of the \(L_1\)-conditional quantiles ⋮ Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density ⋮ Estimating the conditional distribution in functional regression problems ⋮ Local linear estimate of the functional expectile regression

Uses Software

• fda (R)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functional linear regression analysis for longitudinal data
• Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
• Prediction in functional linear regression
• CLT in functional linear regression models
• Local functional principal component analysis
• Weak convergence in the functional autoregressive model
• Smoothing splines estimators for functional linear regression
• Variable bandwidth and local linear regression smoothers
• The Gaussian measure of shifted balls
• Functional data analysis
• Approximation, metric entropy and small ball estimates for Gaussian measures
• Linear processes in function spaces. Theory and applications
• Applied functional data analysis. Methods and case studies
• Optimal global rates of convergence for nonparametric regression
• Equivalence classes of regularly varying functions
• Exact behavior of Gaussian seminorms
• The probability of small Gaussian ellipsoids and associated conditional moments
• Local linear regression smoothers and their minimax efficiencies
• Generalized functional linear models
• Nonparametric regression estimation for dependent functional data: asymptotic normality
• Nonparametric functional data analysis. Theory and practice.
• Locally modelled regression and functional data
• Linear minimax efficiency of local polynomial regression smoothers
• Equivalent Subgradient Versions of Hamiltonian and Euler–Lagrange Equations in Variational Analysis
• A form of regular variation and its application to the domain of attraction of the double exponential distribution